Regularity and well posedness for the Laplace operator on polyhedral domains

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

We announce a well-posedness result for the Laplace equation in weighted
Sobolev spaces on polyhedral domains in $\RR^n$ with Dirichlet boundary
conditions. The weight is the distance to the set of singular boundary points.
We give a detailed sketch of the proof in three dimensions.

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